"Edge slide" for bones?
Is there a way for me to &quot;edge slide&quot; the heads along each bone shaft?

Yes.  Each bone's head and tail lie in a particular axis for that bone-- the Y axis.  So if you select a head and move it in that axis, you'll be edge sliding the head along the bone.
Switch to normal orientation, individual origins pivot.  (In edit mode, normal orientation will use each bone's local axes for the transform, while local orientation will use the armature's local axes.)  Select as many heads or tails as you want.  Translate constrained to Y axis (g Y move mouse confirm for me).